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The energy required to charge a capacitor of $5\,\mu\text{F}$ by connecting it to a d.c. source of $20\,\text{kV}$ is

1. 10 kJ
2. 5 kJ
3. 2 kJ
4. 1 kJ

Correct answer: 1 kJ

Solution

The energy stored in a capacitor is $U=\frac12 CV^2$. Substituting $C=5\times10^{-6}\,\text{F}$ and $V=2\times10^4\,\text{V}$ gives $U=\frac12\times5\times10^{-6}\times(2\times10^4)^2=1000\,\text{J}$. Hence the required energy is $1\,\text{kJ}$.

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